Related papers: The Beta-Bernoulli process and algebraic effects

Statistics and Optimization are foundational to modern Machine Learning. Here, we propose an alternative foundation based on Abstract Algebra, with mathematics that facilitates the analysis of learning. In this approach, the goal of the…

In this paper we examine how concurrency has been embodied in mainstream programming languages. In particular, we rely on the evolutionary talking borrowed from biology to discuss major historical landmarks and crucial concepts that shaped…

The application of automatic transformation processes during the formal development and optimization of programs can introduce encumbrances in the generated code that programmers usually (or presumably) do not write. An example is the…

Due to the increased complexity of software development projects more and more systems are described by models. The sheer size makes it impractical to describe these systems by a single model. Instead many models are developed that provide…

We propose a quantum programming paradigm where all data are familiar classical data, and the only non-classical element is a random number generator that can return results with negative probability. Currently, the vast majority of quantum…

Many classification models produce a probability distribution as the outcome of a prediction. This information is generally compressed down to the single class with the highest associated probability. In this paper, we argue that part of…

This paper builds on recent research that focuses on regression modeling of continuous bounded data, such as proportions measured on a continuous scale. Specifically, it deals with beta regression models with mixed effects from a Bayesian…

Extending the lambda-calculus with a construct for sharing, such as let expressions, enables a special representation of terms: iterated applications are decomposed by introducing sharing points in between any two of them, reducing to the…

In this paper, the relationship between probabilistic graphical models, in particular Bayesian networks, and causal diagrams, also called structural causal models, is studied. Structural causal models are deterministic models, based on…

Abstraction is a fundamental tool for reasoning about complex systems. Program abstraction has been utilized to great effect for analyzing deterministic programs. At the heart of program abstraction is the relationship between a concrete…

In this paper we introduced an algebraic semantics for process algebra in form of abstract data types. For that purpose, we developed a particular type of algebra, the seed algebra, which describes exactly the behavior of a process within a…

We present a randomization-based inferential framework for experiments characterized by a strongly ignorable assignment mechanism where units have independent probabilities of receiving treatment. Previous works on randomization tests often…

Bayesian statistical models allow us to formalise our knowledge about the world and reason about our uncertainty, but there is a need for better procedures to accurately encode its complexity. One way to do so is through compositional…

Logic programs, more specifically, Answer-set programs, can be annotated with probabilities on facts to express uncertainty. We address the problem of propagating weight annotations on facts (eg probabilities) of an ASP to its standard…

Various effects in human cognition, often considered `non-classical', have been argued to be most naturally modelled by quantum-like models of decision making. We extend this approach to describe models of cognition and decision-making in…

Exchangeable random partition processes are the basis for Bayesian approaches to statistical inference in large alphabet settings. On the other hand, the notion of the pattern of a sequence provides an information-theoretic framework for…

The design of an experiment can be always be considered at least implicitly Bayesian, with prior knowledge used informally to aid decisions such as the variables to be studied and the choice of a plausible relationship between the…

Dependent nonparametric processes extend distributions over measures, such as the Dirichlet process and the beta process, to give distributions over collections of measures, typically indexed by values in some covariate space. Such models…

A mathematical framework for Continuous Time Finance based on operator algebraic methods offers a new direct and entirely constructive perspective on the field and leads to new numerical analysis techniques. This is partly a review paper as…

We introduce a formal meta-language for probabilistic programming, capable of expressing both programs and the type systems in which they are embedded. We are motivated here by the desire to allow an AGI to learn not only relevant knowledge…